**Doctor of Philosophy (PhD) in Mathematics**

**Doctor of Philosophy (PhD) in Mathematics**

To earn a PhD in Mathematics one must satisfy the following requirements:

- Completion of all required coursework
- Completion of required written examinations
- Completion of Advancement to Candidacy Oral Examination & Graduate Division paperwork
- Completion of Teaching Experience
- Submission of Doctoral Dissertation & Graduate Division paperwork

When accepted into the doctoral program, the student embarks on a program of formal courses, seminars, and individual study courses to prepare for the Ph.D. written examinations, advancement to candidacy oral examination, and dissertation.

Upon entering the program, students are expected to take Math 210 (Real Analysis), Math 220 (Complex Analysis) and Math 230 (Algebra), which must be passed with a grade of B or better. Students must complete these sequences by the end of the second year.

By the start of the **second** **year**, students must achieve *at least* **two** passes at the **M.S. level** among three exams in Real Analysis, Complex Analysis and Algebra.

By the start of the **third** **year**, students must achieve *at least* **two** passes at the **Ph.D. level** among three exams in Real Analysis, Complex Analysis and Algebra.

To satisfy the exam requirements, students may take the Core Assessment Exams (offered in the Spring of every year) or the Qualifying Exams (offered before the start of the fall quarter) in these areas. Students may not attempt to take an exam in a particular subject area **more than 3 times**. A student who passes a Qualifying examination prior to taking the corresponding course will be exempted from taking the course.

Please Note: Corresponding qualifying exam coursework, MATH 210,220, & 230 cannot be used to satisfy **both** exam **and** coursework requirements (i.e. you can’t ‘double dip’).

Some students may require additional background prior to entering Math 210 and 230. This will be determined by assessment prior to the start of the students’ first year by the Vice Chair for Graduate Studies, upon consultation with the graduate studies committee. Such students will be directed into Math 205 and/or Math 206, during their first year. These students may pass one Comprehensive Exam in the areas of Algebra or Analysis *in lieu* of achieving a M.S. pass on one Core Assessment or Qualifying Exam, which must be satisfied *prior* to the start of the students’ second year. Comprehensive Exams in Analysis and Algebra will be offered once per year in the Spring quarter.

By the end of the second year, students must declare a major specialization from the following areas:

- Algebra
- Analysis
- Applied & Computational Mathematics
- Geometry & Topology
- Logic
- Probability

Students are required to take __two____ series__ of courses from their chosen area (students who later decide to change their area must also take two series of courses from the new area). Additionally, all students must take

**of courses**

__two series__*outside*their declared major area of specialization. Special topics courses within certain areas of specialization and courses counted toward the M.S. degree, (other than MATH 205 & MATH 206), will count toward the fulfillment of the major specialization requirement.

By the beginning of their third year, students must have an advisor specializing in their major area. With the advisor's aid, one should begin to form a committee for the Advancement to Candidacy PhD oral examination. This committee will be approved by the Department on behalf of the Dean of Graduate Studies and the Graduate Council and will have five faculty members. At least *one* (and at most two), of the committee members must be faculty from *outside* the Department. Before the end of the third year, students must have a written proposal, approved by their committee, for the Advancement to Candidacy oral examination. The proposal should explain the role of at least two series of courses from the student's major area of specialization that will be used to satisfy the Advancement to Candidacy requirements. The proposal should also explain the role of additional research reading material as well as providing a plan for investigating specific topics under the direction of the student's advisor(s). Only one of the core courses, MATH 210ABC, 220ABC, and 230ABC may count for the course requirement for Advancement to Candidacy Examinations.

After one meets these requirements, the Graduate Studies Committee recommends to the Dean of Graduate Studies the advancement to candidacy for the PhD. degree. Students should advance to candidacy by the **beginning of their fourth year**. After advancing to candidacy, a student is expected to be fully involved in research toward writing his or her PhD dissertation. Ideally, a student should keep in steady contact/interaction with their doctoral committee. Teaching experience and training is an integral part of the PhD program. All doctoral students are expected to participate in the Department's teaching program, unless otherwise communicated during the admissions process.

The candidate must demonstrate independent, creative research in Mathematics by writing and defending a dissertation that makes a new and valuable contribution to mathematics in the candidate's area of concentration. Upon advancement to candidacy a student must form a thesis committee, a subcommittee of the advancement examination committee, consisting of *at least three* total faculty members, chaired by the student's advisor. The committee guides and supervises the candidate's research, study, and writing of the dissertation; participates in or attends the oral defense of the dissertation; and recommends that the PhD be conferred upon approval of the doctoral dissertation.

The normal time for completion of the PhD is **six** **years**, and the maximum time permitted is **seven** **years** (please note the department may only provide financial support for a **maximum** of **six** **years**).

Completion of the PhD degree must occur within 9 quarters of Advancement to PhD candidacy.

__Areas of Specialization and Their Corresponding Advancement to Candidacy Courses__

PhD students will choose **one** specialization from the following six areas, as offered by the Mathematics Department, which determines coursework requirements. Each area of specialization will have a core course, which the Department will do its best to offer each year. The department will offer other courses every other year, or more frequently depending on student demands and other department priorities.

** Algebra**: Math 230ABC (core), Math 232ABC, Math 233ABC, 234ABC, 235ABC, 239ABC

** Analysis**: Math 210ABC (core), Math 220ABC (core), Math 211ABC, Math 260ABC, Math 295ABC, Math 296

** Applied & Computational Mathematics:** Math 290ABC (core), Math 225ABC, Math 226ABC, Math 227AB, Math 291ABC, Math 295ABC

** Geometry & Topology:** Math 218ABC (core), Math 222ABC, Math 240ABC, Math 245ABC, Math 250ABC

** Logic**: Math 280ABC (core), Math 281ABC, Math 282ABC, Math 285ABC

** Probability**: Math 210ABC, Math 211ABC, Math 270ABC, Math 271ABC, Math 272ABC, Math 274

__*PhD Requirements Summarized*__

*By the beginning of the 2nd year:* Pass at the MS level two exams in real analysis, complex analysis or algebra.

*By end of the 2nd year:* (1) Declare a major specialization; (2) complete the course series 210ABC, 220ABC, 230ABC.

*By the beginning of the 3rd year*: (1) Pass at the PhD level two qualifying exams in real analysis, complex analysis or algebra; (2) Select an advisor specialist in the major area and form a committee for the Advancement to Candidacy oral exam.

*Before the end of the 3rd year:* (1) Have a written proposal, approved by the committee, for the PhD Advancement to Candidacy examination.

*By the beginning of the 4th year:* (1) Advanced to Candidacy at the PhD level; (2) form a thesis committee (that is, a subcommittee of the advancement examination committee)

*Completion of the PhD:* Average completion time is **5.8 years**; maximum time permitted is **seven** **years**. The Department will not financially support students *past* their sixth year in the PhD program. Completion of the PhD degree must occur *within* 9 quarters (three years) of advancement to PhD candidacy.

**Graduate Program in Mathematical and Computation Biology (MCSB)**

The graduate program in Mathematical, Computational Systems Biology (MCSB) is designed to meet to meet the interdisciplinary training challenges of modern biology and function in concert with selected department programs, including the Ph.D. in Mathematics.